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Wave Motion overview

Topic 1 of 6

Propagation and particle motion

A progressive wave carries a disturbance through space. Identify what oscillates locally and distinguish that oscillation from the direction in which the pattern and energy travel.

What oscillates?

A mechanical wave involves particles of a material medium, such as a string or a fluid. The particles oscillate about equilibrium positions. Neighbouring parts exert forces on one another; as they move, work transfers energy through the medium.

An electromagnetic wave involves oscillating electric and magnetic fields in space and time. It can propagate through a vacuum, without a material medium. A curve representing a field does not show particles following that curve.

Classify the wave by comparing oscillation with propagation:

  • Transverse: the oscillation is perpendicular to propagation, as for the displacement of an ideal transverse string wave.
  • Longitudinal: the particle oscillation is parallel to propagation, as for sound in a fluid.

A sinusoidal graph alone does not tell you which type it represents. First read which quantity is plotted and how its physical direction relates to propagation.

Track a particle separately from a crest

In the ideal progressive mechanical-wave model, particles oscillate locally while energy is transferred through the medium. The medium does not advance with each crest. Other bulk flows can occur in real fluids or surface waves; they are not the oscillatory particle motion represented by this model.

Consider a transverse wave travelling right, with amplitude 4.0 mm, wavelength 0.80 m and period 0.20 s. A crest is the position of maximum positive displacement at an instant, not the identity of one particle.

The pattern moves right; the tagged particle stays at x = 0.10 m

The filled circle marks the same particle in all three frames. The hollow diamond tracks the same crest. The small downward arrow gives the tagged particle's instantaneous direction of motion.

t = 0.000 s; tagged displacement +2.83 mm

Right-moving transverse wave at 0.000 secondsThe fixed tagged equilibrium coordinate is 0.10 metres in every frame. Its displacement here is 2.83 millimetres, and its instantaneous velocity is downward. The same positive crest has advanced to 0.20 metres. A vertical dashed reference keeps the tagged horizontal position fixed. The rightward propagation arrow and the downward particle arrow represent different motions. Horizontal position and vertical displacement use different displayed scales, so the apparent profile angle is not a physical deflection angle or a phase angle.0.000.200.400.600.80-40+4TagWave rightDisplacement y / mmEquilibrium position x / m

t = 0.025 s; tagged displacement 0.00 mm

Right-moving transverse wave at 0.025 secondsThe fixed tagged equilibrium coordinate is 0.10 metres in every frame. Its displacement here is 0.00 millimetres, and its instantaneous velocity is downward. The same positive crest has advanced to 0.30 metres. A vertical dashed reference keeps the tagged horizontal position fixed. The rightward propagation arrow and the downward particle arrow represent different motions. Horizontal position and vertical displacement use different displayed scales, so the apparent profile angle is not a physical deflection angle or a phase angle.0.000.200.400.600.80-40+4TagWave rightDisplacement y / mmEquilibrium position x / m

t = 0.050 s; tagged displacement -2.83 mm

Right-moving transverse wave at 0.050 secondsThe fixed tagged equilibrium coordinate is 0.10 metres in every frame. Its displacement here is -2.83 millimetres, and its instantaneous velocity is downward. The same positive crest has advanced to 0.40 metres. A vertical dashed reference keeps the tagged horizontal position fixed. The rightward propagation arrow and the downward particle arrow represent different motions. Horizontal position and vertical displacement use different displayed scales, so the apparent profile angle is not a physical deflection angle or a phase angle.0.000.200.400.600.80-40+4TagWave rightDisplacement y / mmEquilibrium position x / m

The horizontal and vertical display scales differ. Across these 0.050 s, the crest moves 0.20 m right; the tag moves transversely through equilibrium. A crest is a travelling pattern, not a particle carried along the string.

The filled marker follows one particle at the same equilibrium horizontal position. The hollow marker follows the travelling crest. Propagation and particle-velocity arrows have different meanings; horizontal and vertical display scales are different.

At times 0, 0.025 and 0.050 s, the tagged particle at equilibrium position x = 0.10 m has displacements about +2.83, 0 and -2.83 mm. It moves down in all three shown states. Meanwhile, the corresponding crest advances from x = 0.20 to 0.30 to 0.40 m.

Positive displacement means above equilibrium, not necessarily upward velocity. At the first instant, the particle is above equilibrium but moving down. Comparing the successive frames reveals its motion.

Optional check A transverse-wave profile moves right. At the marked particle, the profile rises as you look from left to right, and the particle is above equilibrium. What is happening there in the ideal string-wave model?
A transverse-wave profile moves right. At the marked particle, the profile rises as you look from left to right, and the particle is above equilibrium. What is happening there in the ideal string-wave model?

Electromagnetic fields and propagation

In the plane electromagnetic-wave model, the electric and magnetic fields oscillate perpendicular to one another and to propagation. The electric-field direction is the direction used to describe the wave's polarisation.

Electromagnetic waves involve fields, not a material particle path

Electric field, magnetic field and propagation are mutually perpendicularAt one point and one instant in a plane electromagnetic wave, the electric-field arrow points up, the magnetic field points out of the page and the wave propagates right. The magnetic-field direction is represented by a dot inside a circle at the common reference point. The dot is a field-direction symbol, not a material particle or a current. A right-angle mark separates the in-plane electric-field and propagation directions; the magnetic field is perpendicular to the page. The arrow lengths do not use a common magnitude scale.Electric field EUpPropagationRightMagnetic field BOut of the page

The arrows show directions at one instant. The electric and magnetic fields oscillate; an electromagnetic wave can propagate without a material medium. The circled dot here denotes magnetic field out of the page.

At the indicated instant, electric field is upward, magnetic field is out of the page and propagation is rightward. The out-of-page symbol marks a field direction, not a current or material particle.

The fields reverse during the cycle, while the progressive wave continues in its propagation direction. These field arrows describe local oscillating quantities; they are not paths followed by matter through the diagram.